Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 3 - Determinants - 3.3 Properties of Determinants - 3.3 Exercises - Page 127: 81

Answer

The statement is correct.

Work Step by Step

Let $S$ be a singular matrix of order $n$ and $B$ a matrix of order $n$. Then, we have: $|SB|=|S| |B| $ Since $S$ be a singular matrix of order $n$, then $|S|=0$. Thus, $|SB|=|S| |B| =0$ Therefore, the matrix $SB$ is a singular matrix.
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